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Magnetic investigation of zero-field-cooled dextran-coated
magnetite-based magnetic fluid
P.C. Moraisa,, J.G. Santosa, L.B. Silveiraa, W.C. Nunesb,
J.P. Sinneckerb, M.A. Novakb
a
Universidade de Brası´lia, Instituto de Fı´sica, Fı´sica Aplicada, C.P. 004455, Campus Universitario, Brası´lia-DF 70919 970, Brazil
b
Universidade Federal doRio de Janeiro, Instituto de Fı´sica, 21945-970, Rio de Janeiro-RJ, Brazil
Abstract
In this study, we investigate the temperature dependence of the zero-field-cooled magnetization of a quasimonodisperse dextran-coated magnetite-based magnetic fluid. The well-defined maximum in the magnetization versus
temperature curve and its downshift with the applied external field is explained by a simple model considering thermally
activated dynamics of the nanoparticles magnetic moment and the temperature dependence of the saturation
magnetization.
r 2004 Elsevier B.V. All rights reserved.
PACS: 75.50.Mm; 75.60.Ej; 75.50.Tt
Keywords: Magnetic fluid; Magnetization; Fine-particle system
The magnetic behavior of field-cooled and zero-fieldcooled (ZFC) magnetic fluids (MFs) has attracted the
attention of the scientific community for over a decade
[1–12]. Though most of the experimental data available
in the literature are related to magnetization measurements of systems consisting of magnetic nanoparticles
uniformly dispersed in a carrier liquid [1–8], magnetic
resonance investigations [9–12] have also made contributions to clarify fundamental aspects. In order to
perform magnetic investigations, the MF sample is
cooled down to a frozen state at low temperatures under
applied-field or zero-field condition. The most prominent aspect of the experimental data is the onset of a
Corresponding author. Tel.: +55 61 273 6655;
fax: +55 61 272 3151.
E-mail address: [email protected] (P.C. Morais).
well-defined maximum in the magnetization (M) versus
temperature (T) curve of ZFC MF samples [1–8].
According to Luo et al. [1] the ZFC peak temperature
depends essentially upon both the nanoparticle concentration and the steady magnetic field applied during the
magnetization measurements. The ZFC peak temperature shifts to higher temperatures as the nanoparticle
concentration increases. Furthermore, the ZFC peak
temperature shifts to lower temperatures as the applied
field increases above about 100 Oe. For applied fields
below about 100 Oe, however, the peak temperature
shifts to higher temperatures. In addition to the abovedescribed observations, related to frozen MF samples,
there are similar magnetization versus temperature data
(ZFC peak in the M T curve) reported for magnetic
nanoparticle-based systems, either as powder samples
[13,14] or supported in a solid template [15–17]. The
physical picture commonly used to describe this
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.jmmm.2004.11.051
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behavior takes into account the particle–particle interaction, including the anisotropy effect within a meanfield description [16]. Nevertheless, alternative approaches, which do not require particle–particle interaction, have been used to explain the ZFC peak in MF
samples [3,6,8]. Within the single-particle approximation
used by Morais et al. [8] a well-defined maximum in the
M T curve is mainly due to the temperature dependence of the reorientation of the magnetic moment
associated to the magnetic nanoparticle plus the
temperature dependence of the saturation magnetization. In this work, we use this simple model to describe
the ZFC magnetization curves of a water-based MF
sample containing magnetite nanoparticles surfacecoated with dextran. The MF sample used in this study
was synthesized according to the standard procedure
described in the literature [18]. Transmission electron
microscopy micrographs were used to determine the size
distribution of the obtained nanoparticles. The size
distribution function has the usual log-normal shape
with mean particle diameter of 3.170.1 nm and diameter dispersion of 0.2670.01. The MF sample used in
the experiments contained about 5 1016 particle/cm3.
The magnetization measurements were performed using
a commercial Quantum Design PPMS model 6000
extraction magnetometer. Symbols in Fig. 1 show the
temperature dependence of the ZFC magnetization
under three different applied fields (200, 500 and
1000 Oe). The M T curves were obtained by cooling
the MF sample from room temperature down to 2 K
under zero external fields. Then, a steady magnetic field
(200, 500 and 1000 Oe) was applied to the sample and
the magnetization measurements were performed while
the temperature was increased to 250 K, using the same
constant temperature sweep rate.
The model used to fit the experimental data shown in
Fig. 1 has been successfully applied to explain the ZFC
magnetization curves of ionic MFs [8]. In contrast to the
ionic MFs, however, the M T curves presented here
show broader peaks. In spite of this peculiarity, we
succeeded in using the same model to fit the data
presented in this study. The model starts with the
calculation of the magnetization of an ensemble of N
uniformly dispersed, randomly oriented and identical
magnetic nanoparticles bearing the same magnetic
moment (m) in a frozen carrier fluid. Due to the very
narrow particle size distribution function (diameter
dispersion equals to 0.26) the nanoparticle polydispersity was not included in the calculation. Within this
picture, magnetic moment reversal occurs by thermal
activation and particle–particle interaction was neglected. The frozen ensemble was then submitted to an
external steady field of 200, 500 and 1000 Oe, and the
angular distribution of the magnetic moment of the
particles with respect to both the external field (H) and
the easy axis (e.a.) direction was taken into account in
the calculation of the magnetization:
X
MðTÞ ¼
mi cos ðyi fi Þ;
i
where mi is the magnetic moment associated to the ith
nanoparticle. yi and fi are the angles between the
external field (H) and the magnetic moment (mi) and the
e.a. direction, respectively. Assuming a monodisperse
nanoparticle distribution with all particles bearing a
magnetic moment m, the magnetization reads:
MðTÞ ¼ Nm/ cos ðy fÞS;
where /Smeans statistical average. In order to calculate
/cos(y–f)S we start writing the free energy (E) of a
nanoparticle in terms of both the anisotropy and the
Zeeman component as E(y,f) ¼ KV sin2 fmH cos(y–f), where K and V are the magnetic anisotropy
and the nanoparticle volume, respectively. From the free
energy minimum condition the relationship between y
and f reads:
y ¼ f þ arcsin KV =mH sinð2fÞ :
The /cos(y–f)S term is calculated by
R
cosðy fÞ sin f expðE=kTÞ df
R
/ cosðy fÞS ¼
:
sin f expðE=kTÞ df
Fig. 1. Temperature dependence of the ZFC magnetization of
MF samples (symbols) under different external field values
(200, 500 and 1000 Oe). The solid lines represent the best fit to
the model described in this study.
Finally, the sample magnetization (M S ¼ Nm) is
expressed as M S ¼ M 0 ð12T=T 0 Þb [19].
Solid lines in Fig. 1 represent the best curve fitting of
the M T data according to the model described above.
Values of important parameters, as for instance the ratio
A ¼ m0 H=k; T 0 ; and b obtained from the fitting
procedure are shown in Table 1. The first aspect
concerning the fitted values is the expected linear
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Table 1
Parameters obtained from the fit of the M T data according
to the model described in this work
H (Oe)
A (K)
T0 (K)
b
200
500
1000
12572
13971
18071
36574
46573
60071
0.3170.01
0.3170.01
0.3770.01
dependence of the parameter A with the applied field
(H). The obtained angular coefficient of A versus H was
(7079) K/kOe. The second interesting aspect related to
the values reported in Table 1 is the linear dependence of
T 0 with H. We found for the angular coefficient of T 0
versus H the value of (268.970.9) K/kOe, whereas the
value found for the intercept constant was
(330.970.6) K. Finally, it is interesting to point out
that the fitted exponent b was close to the usual 13 value
for fields below 1 kOe. At 1 kOe, however, b shifted to a
value higher than the 13 mark.
In conclusion, the temperature dependence of the
ZFC magnetization of dextran-coated magnetite-based
MF samples has been investigated in this study. Neither
particle–particle interaction (low particle concentration)
nor the particle size polydispersity profile, the latter
typical of MF samples, is included in the model used to
explain the experimental data. The model does include
the thermal fluctuation of the nanoparticle magnetic
moment (small particle sizes and/or low effective
anisotropy values), the interaction between the magnetic
moment and the applied external field, and the
temperature dependence of the sample magnetization
through a well-know expression. The good fitting of the
data using the model presented here indicates that
dipolar interaction among neighboring nanoparticles
may play a marginal role in determining the most
relevant aspects of the experimental data, i.e. the
maximum in the M T curve and the field dependence
of this maximum.
3
The authors acknowledge the financial support of the
Brazilian agencies CNPq, FINEP, FINATEC, and
Instituto de Nanociências/MCT.
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